This paper is concerned with the problem of robust dichotomy of a Lur'e system with norm constraint structured uncertainties, which represent numerous kinds of uncertainties, including mixed real/complex dynamic uncertainties. Leonov's frequency-domain dichotomy condition for Lur'e systems is generalized to the situation where the linear part of the system includes structured uncertainties. By applying the structured singular value of an operator to structured uncertainty, the results on robust dichotomy analysis of the Lur'e system are obtained. Finally a numerical example is included to demonstrate the validity and the applicability of the proposed approach.